Binomial Distribution Calculator
Answer
The probability of between and successes is .
How to find the answer
The Way Mortal Humans Do It
If you’re like most people, using a formula over and over again to get the answers you want doesn’t sound like fun!
Most people use a binomial distribution table to look up the answer, like the one on this site. The problem with most tables, including the one here, is that it doesn’t cover all possible values of p, or n. So if you have p = .64 and n = 256, you probably won’t be able to simply look it up in a table.
The alternative method is to use a calculator like this one! Many scientific calculators like the TI-89 can find the answer to problems like these.
If you want to know how the numbers work, then read on!
The “Mathy” Way
To figure out what the total probability is, first we have to figure out the probability of each value of x, using this formula:
| n!
x!(n – x)! |
px (1-p)(n-x) |
So if your range is from to , you’d have to use that formula for . Then when you got the answer from each of those, you’d add them all up together to get the total:
P( … ) =
The graph below shows each possible value of x along the bottom, and the bar represents the chance that x will actually equal that value during a real experiment. Yellow bars means the value is in the range you chose, and if you look at the list above, you’ll see the bars correspond to the answers, and you’ll also see that if you added up all the yellow areas, you’d get the total from above also.